I feel it's a bit bad that I normally don't remember themes outside of the battle themes. So all those route and city musics, they just tend to go under my notice. :(
Anyway. As for my favorites:
First one that comes to mind is Giratina's battle music from Platinum:
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https://www.youtube.com/watch?v=odvMnKBBI88
I didn't realize this track existed until I stumbled upon it while randomly looking up pokemon music one day. I had never gotten that far in Platinum to come upon it myself, and...finding it was honestly the reason why I picked my Platinum back up. This track is just...I can't even properly describe it. It's eerie, it's anxious, it loops from fast to slow, it fits Giratina
so well, and it might just be me but I swear I got vibes of Earthbound while listening to it (totally unrelated game, but still awesome in its own right, so to be reminded of that...I approve).
Second, the X/Y Gym Leader battle theme:
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https://www.youtube.com/watch?v=MkZkbbfOEdM
Took me by surprise when I first heard it, since it's definitely a different style from previous gym leader battles. It's not the triumphant blare of "important battle, go get 'em!"; instead, it's a more subtle theme, a tense heartbeat that still somehow manages to get you pumped up for the battle.
Third, B/W Gym Leader battle:
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https://www.youtube.com/watch?v=6K4_aSOexfU
What always gets me is how strong the opening notes are. Yeah I don't really have much more to say about it, I adore the opening notes and then the rest of the song just keeps up that same pace. Just seems stronger than a lot of the other gym battle themes. I love it.
There's more that I like, but those are at least the top three of my current favorites.